Results for Point Group D18h



Symmetric powers of degenerate representation E8g
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C18 2C9 2C6 2(C9)2 2(C18)5 2C3 2(C18)7 2(C9)4 C2 9C'2 9C''2 i 2(S9)5 2(S18)7 2S3 2(S18)5 2(S9)7 2S6 2S9 2S18 σh 9σd 9σv
1 2 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 2 0 0 2 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 2 0 0
2 3 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 3 1 1 3 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 3 1 1
3 4 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 4 0 0 4 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 4 0 0
4 5 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 5 1 1 5 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 5 1 1
5 6 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 6 0 0 6 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 6 0 0
6 7 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 7 1 1 7 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 7 1 1
7 8 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 8 0 0 8 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 8 0 0
8 9 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000 9 1 1 9 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000 9 1 1
9 10 1.000 1.000 1 1.000 1.000 1 1.000 1.000 10 0 0 10 1.000 1.000 1 1.000 1.000 1 1.000 1.000 10 0 0
10 11 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 11 1 1 11 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 11 1 1
11 12 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 12 0 0 12 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 12 0 0
12 13 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 13 1 1 13 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 13 1 1
13 14 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 14 0 0 14 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 14 0 0
14 15 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 15 1 1 15 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 15 1 1
15 16 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 16 0 0 16 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 16 0 0
16 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 17 1 1 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 17 1 1
17 18 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000 18 0 0 18 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000 18 0 0
18 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000 19 1 1 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000 19 1 1
19 20 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 20 0 0 20 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 20 0 0
20 21 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 21 1 1 21 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 21 1 1


Decomposition to irreducible representations
Power
To		 A1g A2g B1g B2g E1g E2g E3g E4g E5g E6g E7g E8g A1u A2u B1u B2u E1u E2u E3u E4u E5u E6u E7u E8u
1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 E8g
2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g
3 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 E6g⊕E8g
4 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g
5 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 E4g⊕E6g⊕E8g
6 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E6g
7 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 E2g⊕E4g⊕E6g⊕E8g
8 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E6g⊕E8g
9 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E2g⊕E4g⊕E6g⊕E8g
10 1 0 0 0 0 1 0 1 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕E6g⊕2E8g
11 1 1 0 0 0 2 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E2g⊕E4g⊕E6g⊕E8g
12 1 0 0 0 0 1 0 1 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕E4g⊕2E6g⊕2E8g
13 1 1 0 0 0 2 0 2 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E2g⊕2E4g⊕E6g⊕E8g
14 1 0 0 0 0 1 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕E2g⊕2E4g⊕2E6g⊕2E8g
15 1 1 0 0 0 2 0 2 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E2g⊕2E4g⊕2E6g⊕E8g
16 1 0 0 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕2E2g⊕2E4g⊕2E6g⊕2E8g
17 1 1 0 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E2g⊕2E4g⊕2E6g⊕2E8g
18 2 1 0 0 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2E2g⊕2E4g⊕2E6g⊕2E8g
19 1 1 0 0 0 2 0 2 0 2 0 3 0 0 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E2g⊕2E4g⊕2E6g⊕3E8g
20 2 1 0 0 0 3 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕3E2g⊕2E4g⊕2E6g⊕2E8g


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement